Place shredded potatoes in cheesecloth and wring out any excess moisture.
Mix potatoes, eggs, flour, onion, and salt together in a bowl.
Heat 1/2 cup oil in a large skillet over medium-high heat until oil shimmers. Working in batches, drop spoonfuls of the potato mixture into the hot oil, pressing each down to form a pancake. Cook latkes until browned and crisp, 3 to 5 minutes per side; transfer to paper towels to drain.
Heat 1 tablespoon oil in a separate skillet over medium-high heat. Cook pears in hot oil and sprinkle 2 tablespoons brown sugar over pears. Cook pears until browned and sugar is melted, 3 to 5 minutes per side.
Place latkes on a serving platter. Top each latke with 1 round of goat cheese and a pear. Sprinkle brown sugar on the pears and drizzle sherry vinegar over the top.